Yes, it's possible if some authority decide to shut down Internet but hope this will never happen.
It's not that complicated.
Remember that woman in Georgia that cut a few cables and two countries were left offline for two days?
The internet is just a bunch of computers hooked with cables , cut 4 or 5 of the most important ones and chaos will rule.
http://gizmodo.com/5912383/how-to-destroy-the-internet
To power up your house you only need your equipment.
Solar panels , wind or gas generators.
In the case of the internet you don't only need your computer and your equipment but you also need the others to have those and in place plus a way of communicating with them.
You can have your own power plant but you can't have your own internet.
Didn't realize the internet required so many "things" to work properly for us to use it. Bitcoin and blockchain are highly depended on the internet to operate without a fuss.
So if internet is to go down, so too will bitcoin and blockchain.